Department of

# Mathematics

Seminar Calendar
for events the day of Friday, November 15, 2019.

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events for the
events containing

More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, November 15, 2019

2:00 pm in 347 Altgeld Hall,Friday, November 15, 2019

#### Tensor Categories Reading Group

###### See seminar site

Abstract: See seminar site.

3:00 pm in 341 Altgeld Hall,Friday, November 15, 2019

#### Heat Kernel Proof of the Lefschetz Fixed Point Theorem

###### Gayana Jayasinghe (UIUC Math)

Abstract: I'll motivate the theorem and present a proof based on the heat kernel, which showcases some nice ideas in spectral geometry

4:00 pm in 141 Altgeld Hall,Friday, November 15, 2019

#### A Small Introduction to Big Concepts in Hyperbolic Manifolds

###### Joseph Malionek (UIUC)

Abstract: Hyperbolic Manifolds appear in some surprising places throughout geometry and topology, but unless you are in a field that requires thorough knowledge of them, you probably don't have the time or energy to learn about them on your own. I want to save you some work by introducing a couple of the bigger concepts and using them to sketch out some of the bigger theorems. An intuitive (but not necessarily formal) knowledge of Riemannian Geometry is assumed.

4:00 pm in 347 Altgeld Hall,Friday, November 15, 2019

#### Classifying Permutations Under Context-Directed Swaps

###### Joseph Rogge (UIUC Math)

Abstract: In 2003, Prescott hypothesized a special sorting operation performed on the genomic material of ciliates. This operation, called cds, involves block interchanges of permuted lists. Christie (1996) discovered that among those permutations which are sortable by cds, cds sorts them using the fewest possible block interchanges of any kind. Adamyk et al. (2013) discovered an efficient way of quantifying the non-cds-sortability of a permutation called the strategic pile. My group partially characterized permutations with maximal strategic pile (in some sense, the permutations for which applying cds is the most unpredictable), completing this characterization when the number of available cds moves is minimal and when it is nearly maximal. We discover a ZnｘZn-action on permutations in S(n+1) that preserves the number of available cds moves. This group action, defined on permutations, has a very nice visual interpretation via chord diagrams (circles with intersecting chords). We characterize the stabilizer of this group action, and are thus able to use Lagrange’s Theorem to count the size of orbits of permutations. This allows us to count the number of permutations with a given number of cds moves.

5:00 pm in 241 Altgeld Hall,Friday, November 15, 2019

#### NO MEETING THIS WEEK!

Abstract: See you next week!